A268622 - OEIS

%I #7 Mar 21 2018 09:46:40

%S 9,42,174,666,2430,8586,29646,100602,336798,1115370,3661038,11927898,

%T 38618046,124357194,398580750,1272269754,4046391774,12827922858,

%U 40550011182,127848761370,402142467582,1262215953162,3954013510734

%N Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

%C Column 2 of A268628.

%H R. H. Hardin, <a href="/A268622/b268622.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 9*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Mar 21 2018: (Start)

%F G.f.: 3*x*(3 - x)*(1 - x) / (1 - 3*x)^2.

%F a(n) = 2*3^(n-2)*(5+8*n) for n>1.

%F (End)

%e Some solutions for n=8:

%e ..1..0. .0..1. .2..1. .1..2. .2..2. .0..1. .0..0. .0..0. .1..0. .1..0

%e ..2..2. .1..0. .1..0. .2..1. .2..2. .1..0. .0..1. .0..1. .2..2. .0..0

%e ..2..1. .2..1. .2..1. .1..2. .1..2. .2..1. .0..0. .0..0. .1..2. .1..2

%e ..2..2. .2..2. .1..0. .2..2. .2..2. .2..2. .1..0. .0..0. .0..1. .2..1

%e ..2..1. .1..2. .2..1. .2..2. .2..1. .2..1. .0..1. .0..0. .1..0. .1..2

%e ..2..2. .2..2. .1..2. .2..1. .2..2. .2..0. .0..0. .1..0. .2..1. .2..2

%e ..1..2. .1..2. .1..2. .1..2. .0..1. .1..0. .1..0. .2..2. .2..2. .1..2

%e ..2..2. .0..0. .0..1. .2..1. .1..2. .0..0. .0..1. .1..2. .1..2. .0..1

%Y Cf. A268628.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 09 2016